Noam Chomsky, a renowned linguist and cognitive scientist, introduced a classification of grammars known as Chomsky’s Hierarchy. This classification categorizes grammars based on their generative power and the complexity of the languages they can generate. Chomsky’s Hierarchy consists of four types of grammars, each associated with a corresponding class of languages:
- Type 0: Unrestricted Grammars (Recursively Enumerable Languages):
- These grammars have no restrictions on production rules.
- They can generate languages that are recognized by Turing machines.
- The languages generated by unrestricted grammars are called recursively enumerable languages.
- These languages can be recognized by a Turing machine, but there is no guarantee of halting for every input.
- Type 1: Context-Sensitive Grammars (Context-Sensitive Languages):
- In context-sensitive grammars, the left-hand side of production rules can have a non-terminal symbol followed by a context (a string of terminals and non-terminals).
- Context-sensitive grammars are more restricted than unrestricted grammars.
- The languages generated by context-sensitive grammars are called context-sensitive languages.
- Context-sensitive languages can be recognized by linear-bounded automata.
- Type 2: Context-Free Grammars (Context-Free Languages):
- Context-free grammars have production rules of the form A → α, where A is a non-terminal symbol, and α is a string of terminals and non-terminals.
- The left-hand side of production rules contains only a single non-terminal symbol.
- Context-free grammars are widely used in describing the syntax of programming languages.
- The languages generated by context-free grammars are called context-free languages.
- Context-free languages can be recognized by pushdown automata.
- Type 3: Regular Grammars (Regular Languages):
- Regular grammars have production rules of the form A → aB or A → a, where A and B are non-terminal symbols, and ‘a’ is a terminal symbol.
- The left-hand side of production rules contains only a single non-terminal symbol, and the right-hand side is either a single terminal symbol, a terminal symbol followed by a non-terminal symbol, or just a non-terminal symbol.
- Regular grammars are the simplest form of grammars and are used to generate regular languages.
- Regular languages can be recognized by finite automata.
The hierarchy represents an increasing level of generative power, with Type 3 grammars being the least powerful and Type 0 grammars being the most powerful. This classification scheme is significant in the study of formal languages and automata theory, providing insights into the complexity of languages and the computational devices required to recognize them.